The Foxes have initiated their quest for a substitute for Youri Tielemans, who is expected to leave the club in the summer.
His contract is due to expire in June, and he shows no indication of agreeing to a fresh agreement. Consequently, there are expectations that the Belgium international will join another team on a free transfer, with Arsenal and Barcelona expressing interest.
Reports from Italy suggest that the Foxes have inquired about Gagliardini from Inter Milan.
The midfielder joined Inter in 2017 and has since made 178 appearances, providing 16 goals and nine assists.
The Italian outfit are unlikely to offer a new deal to the 28-year-old midfielder, and thus he can now initiate talks with other clubs on a pre-contract basis.
As Leicester anticipates losing Tielemans without receiving a fee, pursuing Gagliardini could be a cost-effective strategy to replace the Belgian. However, Galatasaray are also rumoured to have an interest in the Inter man, potentially making it a competitive market for Leicester City.